Abstract

The hierarchically nested structure is widely observed in a broad range of real systems, encompassing ecological networks, economic and trade networks, communication networks, among many others. However, there remain statistical challenges of the prevalence of nestedness. In response to this problem, we focus on the effect of incomplete information and the inputted matrix size, the role of network density and degree sequences, and the relevance of degree-degree correlation to conduct systematic research on the significance of the nested structure according to multiplex world trade networks. Firstly, the nested structure can observe significantly when suffering incomplete information and varying inputted matrix size. Secondly, to analyze the role of network density and degree sequences in nested structure, we use “swappable rows, swappable columns” null model which conserves the network size and density, and “fixed in-degree, fixed out-degree” null model which not only preserves the network size and density but also keeps node degree to do randomization tests of nestedness. The randomizations of two null models remark that most nested structures are not determined by network density and degree sequences but closely related to them. Finally, we investigate degree-degree correlation in nested networks, and the results show that the nested structure is negatively related with degree-degree correlation of the network. Following the empirical analysis train of thought, we argue that nestedness is still a unique feature of the network.